Radiation detector systems and germanium detector systems, in particular, are generally efficiency calibrated using radioactive standards that resemble the actual samples as closely as possible in terms of size, shape, composition, and relative position between the detector and the sample (the source-detector geometry).
Gamma spectroscopy systems use a variety of detector types. Common types are NaI(Tl) and Ge. These detector systems are generally calibrated for energy vs. efficiency using radioactive standards that resemble the actual samples as closely as possible in terms of size, shape, composition, and relative position between the detector and the sample [the source-detector geometry].
In the laboratory application, samples are placed in containers and measured. But since most laboratories use many different types of sample containers, and may also use each one of them at several detector-to-sample distances, and generally many different sample matrix compositions, the efficiency calibration is both an expensive and a time consuming task.
But, in many environmental and other situations, the object to be measured are generally large. The most common current method is to take small samples of these large objects, and assay them in the standardized and calibrated geometries at the laboratory. But this both expensive and time consuming since it involves collecting the sample, packaging it, transporting it to the laboratory, preparing the sample, and finally assaying it. Furthermore, there is always the question of how representative the samples are of the larger object and how to deal with large solid objects that do not lend themselves to sampling. In situ gamma spectroscopy is much more direct; just take the laboratory detector to the object, and assay the entire object. This has the advantage of lower cost for the measurement, and nearly instantaneous results.
But, then the detector must be calibrated for these large objects. Building laboratory sized radioactive calibrations sources is a solvable problem, but building very large ones is very difficult, very expensive, creates radioactive waste, and perhaps not very safe. And, if the sample is in a low efficiency geometry, [e.g. behind a shield, at a far distance, etc.] then the radioactive calibration source must be very "hot", which makes all the previous problems very much greater.
For certain types of measurements, it is very difficult, or impossible to create a standard source that truly mimics the actual sample. Such difficult measurements include very large containers, in which a uniform distribution of the radioactive standard material is very difficult to assure. Another common item to be measured in situ is soil, in which the distribution of the radioactivity of interest is not uniform, but varies exponentially with depth in the soil. This is nearly impossible to mimic using an exact radioactive calibration source. Today, in such cases, the efficiency calibration is commonly created from a series of radioactive standard point source measurements that establish the detector response at various angles between the detector axis and a point source. This angular response is then expanded into an efficiency calibration for a semi-infinite plane at a specific distance from the detector, typically at 1 meter using mathematical integration techniques. This type of calibration methodology has been pioneered by the DOE Environmental Measurement Laboratory (EML) in New York in their various reports and publications. A description of the theory and application can be found in HASL-258 (H. L. Beck et al., USDOE Report HASL-258, 1972) and of the more detailed calibration procedures in HASL-300 (N. A. Chieco et al. (eds.), USDOE Report, HASL-300, 27th edition, Vol. 1, Section 3, 1992). Where a full characterization of a detector is not practical, an approximation may be used (I. K. Helfer and K. M. Miller, Health Physics, 55 (1988) 15).
The EML method is not applicable for close geometries, for non-symmetric geometries, or for complex geometries. Over the years, mathematical methods for calibration in place of measuring radioactive standards have been suggested for some specific cases. The point, line and area approximations and the related calibrations for performing holdup measurements in simplified geometries are described in the NUREG/CR-5550 book (D. Reilly, et. al. (eds.), NUREG/CR-5550, 1991). These methods allow multiple radioactive standard point source measurements to be mathematically integrated to represent line or area sources. However, the approximations made in these methods make them to be of a very limited use for complex shapes. Filss (P. Filss, Appl. Radiat. Isot. 46, (1995) 805) describes a method of using a reference radioactive calibration source, and a mathematical absorption correction to represent a cylindrical waste drum, but his implementation is only applicable to a drum shaped sample.
A general mathematical description of voluminous source activity detection was described by Moens et al in 1981 (L. Moens, et. al., Nucl. Instr. Meth. 187 (1981) 451). However, the method requires detailed detector shape information that is often not available and very long computation times on the computer. To reduce the computational requirements, it has also been suggested that both the sample and the detector be reduced to an effective point with an attenuator in between (M. Noguchi, et. al., Int. J. Appl. Radiat. Isot. 32 (1981) 17). However, this approach still requires a very large number of empirical measurements to establish the effective center of the detector crystal. It also includes many empirical parameters to be determined with good accuracy and that leads to long count times for each of these measurements. Atrashkevich and Kolotov (V. V. Atrashkevich and V. P. Kolotov, J. Radioanal. Nucl. Chem. 169 (1993) 397) have taken this approach further by introducing a special LPT sequence (I. M. Sobol' and R. B. Statnikov, Nauka Press, Moscow, 1981) to maximize the information obtained from such calibration measurements. But their approach still requires the use of many radioactive source measurements, and is limited to only the front hemisphere of a detector and to source-to-detector distances of no more than 10 cm. A semi-computational model has also been used by Aaltonen and her co-workers (H. Aaltonen et. al., Nucl. Instr. Meth. A339 (1994) 87).
It has also been proposed that the calibration measurements be replaced with mathematical simulations such as using Monte Carlo techniques. Rogers (D. W. O. Rogers, Nucl. Instr. Meth. 199 (1982) 531) shows some success with Monte Carlo modeling, but has difficulty with the absolute efficiency calibration for Ge detectors. Debertin and Grosswendt (K. Debertin and B. Grosswendt, Nucl. Instr. Meth. 203 (1982) 343) also use Monte Carlo methods with some success, but rely on a known radioactive source for the primary calibration, and only use the mathematical computation for some correction factors. Nakamura and Suzuki (T. Nakamura and T. Suzuki, Nucl. Instr. Meth. 205 (1983) 211) obtained better results with primary Monte Carlo calculations, but this was only for simple high efficiency geometries. Good results for simple high efficiency geometries have also been obtained by Kamboj and Kahn (S. Kamboj and B. Kahn, Health Physics 70 (1996) 512). However, the computational requirements are very significant and make this approach impractical for a general purpose case. F. Bronson and L. Wang (F. Bronson and L. Wang, Proceedings of Waste Management 96, February 1996, Tucson Ariz.) document the satisfactory use of this Monte Carlo code as a primary calibration technique for a wide variety of simple and complex geometries. But, again, the modeling time and computation time are very extensive.
For certain types of samples, the various approaches described above have provided a solution. If the sample geometry does not change from sample to sample, if the detector physical parameters are well known, and if the source-detector geometry is such that the Monte Carlo computations can proceed quickly, then a one time investment in the calibration effort with Monte Carlo codes may well be worth it.
Accordingly, it is a principal object of the present invention to provide a method for the mathematical characterization of a detector without the use of any radioactive sources.
It is a further object of the invention to provide such a method that can compute specific sample efficiencies in from a few seconds to a few minutes.
It is an additional object of the invention to provide such a method that is applicable to a wide variety of sample shapes and sample-to-detector orientations.
Other objects of the present invention, as well as particular features, elements, and advantages thereof, will be elucidated in, or be apparent from, the following description.